1. Field of the Invention
The present invention relates to a pipe electromagnetic field simulation apparatus which is used to detect a flaw existing in a pipe.
2. Description of the Related Art
Where a flaw existing in a pipe is to be detected, there has been known a method of detecting the flaw in the pipe by moving a transmitting coil for generating a magnetic field while moving a receiving coil for receiving the magnetic field in a manner corresponding with the transmitting coil.
The transmitting coil generates a magnetic field with a predetermined magnitude, thereby causing an eddy current to flow in the pipe. The flow of the eddy current causes an indirect magnetic field to be generated near the pipe. The receiving coil detects the indirect magnetic field. If the pipe has a flaw, then the magnitude and phase of the magnetic field received will change as compared with that without flaw. By picking up the change in magnitude and phase of the magnetic field, the size and phase of the flaw of the pipe are detected.
However, the above-mentioned detecting method has had a problem in that a pipe to be detected has various sizes, whereby a transmitting coil and a receiving coil which are just fit for the size of the pipe must be produced each time the detection is performed, and many experiments be conducted to obtain the relationship with a flaw.
A method of detecting the relationship of a transmitting coil and a receiving coil with a flaw by a simulation technique may be assumed. However, the method and the like which are simple applications of conventional analysis techniques may not be performed successfully because of the following reason.
A pipe is made of an electrically-conductive material. A depth .delta. to which electromagnetic field penetrates an electrically-conductive material is generally represented by the following equation. EQU .delta.=.sqroot.(2/(.omega..sigma..mu.))=1/.sqroot.(3.95.times.10.sup.-6 .times.f.sigma..mu.s) [m]
where .delta.=a depth at which magnitude of electromagnetic field incident on electrically-conductive material attenuates to 1/e (e=2.718 . . . ) of magnitude at surface of electrically-conductive material
.omega.=2.pi.f PA1 f=frequency PA1 .sigma.=electric conductivity(S/m) PA1 .mu.s=specific permeability PA1 input means for inputting various data relating at least to a pipe to be detected for flaw, to a transmitting coil, to the exciting frequency of the transmitting coil, and to a flaw, PA1 non-flaw analysis means for analyzing the electromagnetic field distribution of the pipe assuming that the pipe has no flaw based on the various data from the input means, PA1 first equivalent current source calculation means for determining a current source equivalent to the flaw by utilizing the various data inputted from the input means and the results analyzed by the non-flaw analysis means, and by performing repeatedly a calculation according to Born's approximation rule, and PA1 pipe electromagnetic field analysis means for analyzing the electromagnetic field of the pipe having the flaw by utilizing the results calculated by the first equivalent current source calculation means. PA1 input means for inputting various data relating at least to the pipe, to the transmitting coil, to the exciting frequency of the transmitting coil, and to the flaw, PA1 non-flaw analysis means for analyzing the electromagnetic field distribution of the pipe by assuming that the pipe has no flaw based on the various data from the input means, PA1 second equivalent current source calculation means; PA1 pipe electromagnetic field analysis means for analyzing the electromagnetic field of the pipe having the flaw by utilizing the results calculated by the second equivalent current source calculation means. PA1 input means for inputting various data relating at least to a pipe to be detected for a flaw, to a transmitting coil, to the exciting frequency of the transmitting coil, to a flaw, to a receiving coil, and to a distance between the transmitting coil and the receiving coil, PA1 non-flaw analysis means for analyzing the electromagnetic field distribution of the pipe assuming that the pipe has no flaw based on the various data from the input means, PA1 first equivalent current source calculation means for determining a current source equivalent to the flaw by utilizing the various data inputted from the input means and the results analyzed by the non-flaw analysis means, and by performing repeatedly a calculation according to Born's approximation rule, PA1 pipe electromagnetic field analysis means for analyzing the electromagnetic field of the pipe having the flaw by utilizing the results calculated by the first equivalent current source calculation means, and PA1 flaw signal detecting means for calculating a flaw signal produced in the receiving coil by utilizing the results calculated by the pipe electromagnetic field analysis means. PA1 input means for inputting various data relating at least to the pipe, to the transmitting coil, to the exciting frequency of the transmitting coil, to the flaw, to a receiving coil, and to a distance between the transmitting coil and the receiving coil, PA1 non-flaw analysis means for analyzing the electromagnetic field distribution of the pipe by assuming that the pipe has no flaw based on the various data from the input means, PA1 second equivalent current source calculation means;
For a steel pipe with .sigma.=3.30.times.10.sup.6 and .mu. s=400, its penetration depth .delta. becomes as very small as 1.95.times.10.sup.-3 (m). This mean that steel pipes have a strong magnetic property, whereby a large shield effect is produced and thus the generation of eddy current is biased inward. On the other hand, a corroded flaw occurring on gas pipes is likely to appear on their external surface. Accordingly, the eddy current due to the corroded flaw varies very slightly.
Because of such conditions, in order to analyze a steel pipe by utilizing, for example, the boundary element method, it is necessary to divide the surface of the pipe by a triangle having a side of about 2 mm. This means that in order to analyze, for example, a pipe having a diameter 5 cm and a length 30 cm, it is necessary to divide its lateral length by 75 (50.times.3.14.div.2) and its longitudinal length by 150 (300.div.2). Accordingly, it is necessary to divide the surface into about 10,000 elements with square mesh, or into 20,000 elements with triangle mesh, that is, in total about 40,000 elements for its external and internal surfaces. However, where the boundary element analysis is performed by using a supercomputer, its upper limit is about 5,000 elements, so that the analysis is practically impossible.